Quantum Computer Circuit Analysis and Design

摘要

Recent developments in the Riemannian geometry of quantum computation offer a new approach to the analysis of quantum computation. A geodesic equation defined on the SU(2n) group manifold, representing quantum gate operations on n qubits, may be used to determine optimal quantum evolutions and minimum-complexity quantum circuits. The geodesic equation is a first order nonlinear differential matrix equation of the Lax type. This report gives derivations of the Levi-Civita connection, Riemann curvature, sectional curvature, and geodesic equation on the SU(2n) Riemannian manifold.